LMFDB - Embedded newform 4034.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.82194 q^{3} +1.00000 q^{4} -1.46398 q^{5} +2.82194 q^{6} +3.02991 q^{7} -1.00000 q^{8} +4.96334 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.82194 q^{3} +1.00000 q^{4} -1.46398 q^{5} +2.82194 q^{6} +3.02991 q^{7} -1.00000 q^{8} +4.96334 q^{9} +1.46398 q^{10} -6.50685 q^{11} -2.82194 q^{12} -4.43326 q^{13} -3.02991 q^{14} +4.13125 q^{15} +1.00000 q^{16} -6.53706 q^{17} -4.96334 q^{18} -1.63213 q^{19} -1.46398 q^{20} -8.55023 q^{21} +6.50685 q^{22} -2.19016 q^{23} +2.82194 q^{24} -2.85677 q^{25} +4.43326 q^{26} -5.54041 q^{27} +3.02991 q^{28} -1.73018 q^{29} -4.13125 q^{30} -5.54987 q^{31} -1.00000 q^{32} +18.3619 q^{33} +6.53706 q^{34} -4.43572 q^{35} +4.96334 q^{36} +4.87651 q^{37} +1.63213 q^{38} +12.5104 q^{39} +1.46398 q^{40} -6.60449 q^{41} +8.55023 q^{42} -1.91376 q^{43} -6.50685 q^{44} -7.26621 q^{45} +2.19016 q^{46} +7.13736 q^{47} -2.82194 q^{48} +2.18037 q^{49} +2.85677 q^{50} +18.4472 q^{51} -4.43326 q^{52} +1.62511 q^{53} +5.54041 q^{54} +9.52588 q^{55} -3.02991 q^{56} +4.60577 q^{57} +1.73018 q^{58} -10.9135 q^{59} +4.13125 q^{60} +3.73230 q^{61} +5.54987 q^{62} +15.0385 q^{63} +1.00000 q^{64} +6.49020 q^{65} -18.3619 q^{66} -14.0409 q^{67} -6.53706 q^{68} +6.18050 q^{69} +4.43572 q^{70} -7.17329 q^{71} -4.96334 q^{72} -14.9201 q^{73} -4.87651 q^{74} +8.06163 q^{75} -1.63213 q^{76} -19.7152 q^{77} -12.5104 q^{78} +1.93882 q^{79} -1.46398 q^{80} +0.744700 q^{81} +6.60449 q^{82} -3.85911 q^{83} -8.55023 q^{84} +9.57010 q^{85} +1.91376 q^{86} +4.88247 q^{87} +6.50685 q^{88} +17.6573 q^{89} +7.26621 q^{90} -13.4324 q^{91} -2.19016 q^{92} +15.6614 q^{93} -7.13736 q^{94} +2.38940 q^{95} +2.82194 q^{96} +14.0099 q^{97} -2.18037 q^{98} -32.2957 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.82194	−1.62925	−0.814623	−	0.579990i	$-0.803056\pi$
$3$	−2.82194	−1.62925	−0.814623	+	0.579990i	$0.803056\pi$
$4$	1.00000	0.500000
$5$	−1.46398	−0.654710	−0.327355	−	0.944901i	$-0.606157\pi$
$5$	−1.46398	−0.654710	−0.327355	+	0.944901i	$0.606157\pi$
$6$	2.82194	1.15205
$7$	3.02991	1.14520	0.572600	−	0.819835i	$-0.305935\pi$
$7$	3.02991	1.14520	0.572600	+	0.819835i	$0.305935\pi$
$8$	−1.00000	−0.353553
$9$	4.96334	1.65445
$10$	1.46398	0.462950
$11$	−6.50685	−1.96189	−0.980945	−	0.194285i	$-0.937761\pi$
$11$	−6.50685	−1.96189	−0.980945	+	0.194285i	$0.937761\pi$
$12$	−2.82194	−0.814623
$13$	−4.43326	−1.22957	−0.614783	−	0.788696i	$-0.710756\pi$
$13$	−4.43326	−1.22957	−0.614783	+	0.788696i	$0.710756\pi$
$14$	−3.02991	−0.809778
$15$	4.13125	1.06668
$16$	1.00000	0.250000
$17$	−6.53706	−1.58547	−0.792735	−	0.609567i	$-0.791343\pi$
$17$	−6.53706	−1.58547	−0.792735	+	0.609567i	$0.791343\pi$
$18$	−4.96334	−1.16987
$19$	−1.63213	−0.374437	−0.187218	−	0.982318i	$-0.559947\pi$
$19$	−1.63213	−0.374437	−0.187218	+	0.982318i	$0.559947\pi$
$20$	−1.46398	−0.327355
$21$	−8.55023	−1.86581
$22$	6.50685	1.38727
$23$	−2.19016	−0.456680	−0.228340	−	0.973581i	$-0.573330\pi$
$23$	−2.19016	−0.456680	−0.228340	+	0.973581i	$0.573330\pi$
$24$	2.82194	0.576026
$25$	−2.85677	−0.571354
$26$	4.43326	0.869435
$27$	−5.54041	−1.06625
$28$	3.02991	0.572600
$29$	−1.73018	−0.321287	−0.160643	−	0.987013i	$-0.551357\pi$
$29$	−1.73018	−0.321287	−0.160643	+	0.987013i	$0.551357\pi$
$30$	−4.13125	−0.754260
$31$	−5.54987	−0.996786	−0.498393	−	0.866951i	$-0.666076\pi$
$31$	−5.54987	−0.996786	−0.498393	+	0.866951i	$0.666076\pi$
$32$	−1.00000	−0.176777
$33$	18.3619	3.19640
$34$	6.53706	1.12110
$35$	−4.43572	−0.749774
$36$	4.96334	0.827223
$37$	4.87651	0.801693	0.400847	−	0.916145i	$-0.368716\pi$
$37$	4.87651	0.801693	0.400847	+	0.916145i	$0.368716\pi$
$38$	1.63213	0.264767
$39$	12.5104	2.00327
$40$	1.46398	0.231475
$41$	−6.60449	−1.03145	−0.515724	−	0.856755i	$-0.672477\pi$
$41$	−6.60449	−1.03145	−0.515724	+	0.856755i	$0.672477\pi$
$42$	8.55023	1.31933
$43$	−1.91376	−0.291845	−0.145923	−	0.989296i	$-0.546615\pi$
$43$	−1.91376	−0.291845	−0.145923	+	0.989296i	$0.546615\pi$
$44$	−6.50685	−0.980945
$45$	−7.26621	−1.08318
$46$	2.19016	0.322922
$47$	7.13736	1.04109	0.520545	−	0.853834i	$-0.325729\pi$
$47$	7.13736	1.04109	0.520545	+	0.853834i	$0.325729\pi$
$48$	−2.82194	−0.407312
$49$	2.18037	0.311482
$50$	2.85677	0.404009
$51$	18.4472	2.58312
$52$	−4.43326	−0.614783
$53$	1.62511	0.223226	0.111613	−	0.993752i	$-0.464398\pi$
$53$	1.62511	0.223226	0.111613	+	0.993752i	$0.464398\pi$
$54$	5.54041	0.753955
$55$	9.52588	1.28447
$56$	−3.02991	−0.404889
$57$	4.60577	0.610050
$58$	1.73018	0.227184
$59$	−10.9135	−1.42082	−0.710409	−	0.703789i	$-0.751490\pi$
$59$	−10.9135	−1.42082	−0.710409	+	0.703789i	$0.751490\pi$
$60$	4.13125	0.533342
$61$	3.73230	0.477872	0.238936	−	0.971035i	$-0.423201\pi$
$61$	3.73230	0.477872	0.238936	+	0.971035i	$0.423201\pi$
$62$	5.54987	0.704834
$63$	15.0385	1.89467
$64$	1.00000	0.125000
$65$	6.49020	0.805010
$66$	−18.3619	−2.26020
$67$	−14.0409	−1.71537	−0.857684	−	0.514177i	$-0.828098\pi$
$67$	−14.0409	−1.71537	−0.857684	+	0.514177i	$0.828098\pi$
$68$	−6.53706	−0.792735
$69$	6.18050	0.744045
$70$	4.43572	0.530170
$71$	−7.17329	−0.851312	−0.425656	−	0.904885i	$-0.639957\pi$
$71$	−7.17329	−0.851312	−0.425656	+	0.904885i	$0.639957\pi$
$72$	−4.96334	−0.584935
$73$	−14.9201	−1.74626	−0.873131	−	0.487486i	$-0.837914\pi$
$73$	−14.9201	−1.74626	−0.873131	+	0.487486i	$0.837914\pi$
$74$	−4.87651	−0.566883
$75$	8.06163	0.930877
$76$	−1.63213	−0.187218
$77$	−19.7152	−2.24676
$78$	−12.5104	−1.41652
$79$	1.93882	0.218135	0.109067	−	0.994034i	$-0.465214\pi$
$79$	1.93882	0.218135	0.109067	+	0.994034i	$0.465214\pi$
$80$	−1.46398	−0.163678
$81$	0.744700	0.0827444
$82$	6.60449	0.729344
$83$	−3.85911	−0.423592	−0.211796	−	0.977314i	$-0.567931\pi$
$83$	−3.85911	−0.423592	−0.211796	+	0.977314i	$0.567931\pi$
$84$	−8.55023	−0.932906
$85$	9.57010	1.03802
$86$	1.91376	0.206366
$87$	4.88247	0.523455
$88$	6.50685	0.693633
$89$	17.6573	1.87167	0.935836	−	0.352436i	$-0.114647\pi$
$89$	17.6573	1.87167	0.935836	+	0.352436i	$0.114647\pi$
$90$	7.26621	0.765926
$91$	−13.4324	−1.40810
$92$	−2.19016	−0.228340
$93$	15.6614	1.62401
$94$	−7.13736	−0.736162
$95$	2.38940	0.245148
$96$	2.82194	0.288013
$97$	14.0099	1.42249	0.711246	−	0.702943i	$-0.248131\pi$
$97$	14.0099	1.42249	0.711246	+	0.702943i	$0.248131\pi$
$98$	−2.18037	−0.220251
$99$	−32.2957	−3.24584
$100$	−2.85677	−0.285677
$101$	−17.4527	−1.73661	−0.868303	−	0.496034i	$-0.834789\pi$
$101$	−17.4527	−1.73661	−0.868303	+	0.496034i	$0.834789\pi$
$102$	−18.4472	−1.82654
$103$	8.61001	0.848369	0.424185	−	0.905576i	$-0.360561\pi$
$103$	8.61001	0.848369	0.424185	+	0.905576i	$0.360561\pi$
$104$	4.43326	0.434717
$105$	12.5173	1.22157
$106$	−1.62511	−0.157845
$107$	−18.7433	−1.81198	−0.905990	−	0.423300i	$-0.860872\pi$
$107$	−18.7433	−1.81198	−0.905990	+	0.423300i	$0.860872\pi$
$108$	−5.54041	−0.533127
$109$	−13.3799	−1.28156	−0.640780	−	0.767724i	$-0.721389\pi$
$109$	−13.3799	−1.28156	−0.640780	+	0.767724i	$0.721389\pi$
$110$	−9.52588	−0.908257
$111$	−13.7612	−1.30616
$112$	3.02991	0.286300
$113$	−9.12519	−0.858425	−0.429213	−	0.903203i	$-0.641209\pi$
$113$	−9.12519	−0.858425	−0.429213	+	0.903203i	$0.641209\pi$
$114$	−4.60577	−0.431370
$115$	3.20635	0.298993
$116$	−1.73018	−0.160643
$117$	−22.0038	−2.03425
$118$	10.9135	1.00467
$119$	−19.8067	−1.81568
$120$	−4.13125	−0.377130
$121$	31.3391	2.84901
$122$	−3.73230	−0.337907
$123$	18.6375	1.68048
$124$	−5.54987	−0.498393
$125$	11.5021	1.02878
$126$	−15.0385	−1.33973
$127$	−19.6183	−1.74084	−0.870420	−	0.492310i	$-0.836153\pi$
$127$	−19.6183	−1.74084	−0.870420	+	0.492310i	$0.836153\pi$
$128$	−1.00000	−0.0883883
$129$	5.40050	0.475488
$130$	−6.49020	−0.569228
$131$	14.9845	1.30920	0.654601	−	0.755974i	$-0.272837\pi$
$131$	14.9845	1.30920	0.654601	+	0.755974i	$0.272837\pi$
$132$	18.3619	1.59820
$133$	−4.94522	−0.428805
$134$	14.0409	1.21295
$135$	8.11104	0.698087
$136$	6.53706	0.560548
$137$	−19.9718	−1.70630	−0.853152	−	0.521662i	$-0.825312\pi$
$137$	−19.9718	−1.70630	−0.853152	+	0.521662i	$0.825312\pi$
$138$	−6.18050	−0.526119
$139$	21.5488	1.82775	0.913873	−	0.406000i	$-0.133077\pi$
$139$	21.5488	1.82775	0.913873	+	0.406000i	$0.133077\pi$
$140$	−4.43572	−0.374887
$141$	−20.1412	−1.69619
$142$	7.17329	0.601969
$143$	28.8466	2.41227
$144$	4.96334	0.413611
$145$	2.53295	0.210350
$146$	14.9201	1.23479
$147$	−6.15288	−0.507481
$148$	4.87651	0.400847
$149$	−23.6769	−1.93968	−0.969842	−	0.243736i	$-0.921627\pi$
$149$	−23.6769	−1.93968	−0.969842	+	0.243736i	$0.921627\pi$
$150$	−8.06163	−0.658230
$151$	9.82987	0.799944	0.399972	−	0.916527i	$-0.369020\pi$
$151$	9.82987	0.799944	0.399972	+	0.916527i	$0.369020\pi$
$152$	1.63213	0.132383
$153$	−32.4456	−2.62307
$154$	19.7152	1.58870
$155$	8.12488	0.652606
$156$	12.5104	1.00163
$157$	−9.91111	−0.790993	−0.395496	−	0.918468i	$-0.629427\pi$
$157$	−9.91111	−0.790993	−0.395496	+	0.918468i	$0.629427\pi$
$158$	−1.93882	−0.154245
$159$	−4.58596	−0.363690
$160$	1.46398	0.115738
$161$	−6.63600	−0.522990
$162$	−0.744700	−0.0585091
$163$	−11.5771	−0.906787	−0.453393	−	0.891311i	$-0.649787\pi$
$163$	−11.5771	−0.906787	−0.453393	+	0.891311i	$0.649787\pi$
$164$	−6.60449	−0.515724
$165$	−26.8815	−2.09272
$166$	3.85911	0.299525
$167$	−0.324636	−0.0251211	−0.0125606	−	0.999921i	$-0.503998\pi$
$167$	−0.324636	−0.0251211	−0.0125606	+	0.999921i	$0.503998\pi$
$168$	8.55023	0.659664
$169$	6.65383	0.511833
$170$	−9.57010	−0.733993
$171$	−8.10082	−0.619485
$172$	−1.91376	−0.145923
$173$	−5.38821	−0.409658	−0.204829	−	0.978798i	$-0.565664\pi$
$173$	−5.38821	−0.409658	−0.204829	+	0.978798i	$0.565664\pi$
$174$	−4.88247	−0.370139
$175$	−8.65577	−0.654315
$176$	−6.50685	−0.490473
$177$	30.7973	2.31486
$178$	−17.6573	−1.32347
$179$	14.8329	1.10866	0.554331	−	0.832296i	$-0.312974\pi$
$179$	14.8329	1.10866	0.554331	+	0.832296i	$0.312974\pi$
$180$	−7.26621	−0.541591
$181$	−8.95412	−0.665555	−0.332777	−	0.943005i	$-0.607986\pi$
$181$	−8.95412	−0.665555	−0.332777	+	0.943005i	$0.607986\pi$
$182$	13.4324	0.995676
$183$	−10.5323	−0.778572
$184$	2.19016	0.161461
$185$	−7.13910	−0.524877
$186$	−15.6614	−1.14835
$187$	42.5357	3.11052
$188$	7.13736	0.520545
$189$	−16.7870	−1.22107
$190$	−2.38940	−0.173345
$191$	19.7490	1.42899	0.714494	−	0.699641i	$-0.246657\pi$
$191$	19.7490	1.42899	0.714494	+	0.699641i	$0.246657\pi$
$192$	−2.82194	−0.203656
$193$	5.61538	0.404204	0.202102	−	0.979365i	$-0.435223\pi$
$193$	5.61538	0.404204	0.202102	+	0.979365i	$0.435223\pi$
$194$	−14.0099	−1.00585
$195$	−18.3149	−1.31156
$196$	2.18037	0.155741
$197$	−15.3217	−1.09162	−0.545811	−	0.837908i	$-0.683778\pi$
$197$	−15.3217	−1.09162	−0.545811	+	0.837908i	$0.683778\pi$
$198$	32.2957	2.29516
$199$	2.13728	0.151508	0.0757540	−	0.997127i	$-0.475864\pi$
$199$	2.13728	0.151508	0.0757540	+	0.997127i	$0.475864\pi$
$200$	2.85677	0.202004
$201$	39.6225	2.79476
$202$	17.4527	1.22797
$203$	−5.24230	−0.367937
$204$	18.4472	1.29156
$205$	9.66883	0.675300
$206$	−8.61001	−0.599888
$207$	−10.8705	−0.755553
$208$	−4.43326	−0.307392
$209$	10.6200	0.734604
$210$	−12.5173	−0.863778
$211$	9.11310	0.627372	0.313686	−	0.949527i	$-0.398436\pi$
$211$	9.11310	0.627372	0.313686	+	0.949527i	$0.398436\pi$
$212$	1.62511	0.111613
$213$	20.2426	1.38700
$214$	18.7433	1.28126
$215$	2.80169	0.191074
$216$	5.54041	0.376977
$217$	−16.8156	−1.14152
$218$	13.3799	0.906200
$219$	42.1035	2.84509
$220$	9.52588	0.642235
$221$	28.9805	1.94944
$222$	13.7612	0.923592
$223$	2.83838	0.190072	0.0950359	−	0.995474i	$-0.469703\pi$
$223$	2.83838	0.190072	0.0950359	+	0.995474i	$0.469703\pi$
$224$	−3.02991	−0.202445
$225$	−14.1791	−0.945275
$226$	9.12519	0.606998
$227$	−12.8931	−0.855743	−0.427872	−	0.903839i	$-0.640736\pi$
$227$	−12.8931	−0.855743	−0.427872	+	0.903839i	$0.640736\pi$
$228$	4.60577	0.305025
$229$	−4.75894	−0.314480	−0.157240	−	0.987560i	$-0.550260\pi$
$229$	−4.75894	−0.314480	−0.157240	+	0.987560i	$0.550260\pi$
$230$	−3.20635	−0.211420
$231$	55.6351	3.66052
$232$	1.73018	0.113592
$233$	−24.6821	−1.61698	−0.808490	−	0.588509i	$-0.799715\pi$
$233$	−24.6821	−1.61698	−0.808490	+	0.588509i	$0.799715\pi$
$234$	22.0038	1.43843
$235$	−10.4489	−0.681613
$236$	−10.9135	−0.710409
$237$	−5.47124	−0.355395
$238$	19.8067	1.28388
$239$	4.15919	0.269036	0.134518	−	0.990911i	$-0.457051\pi$
$239$	4.15919	0.269036	0.134518	+	0.990911i	$0.457051\pi$
$240$	4.13125	0.266671
$241$	21.2315	1.36764	0.683820	−	0.729651i	$-0.260318\pi$
$241$	21.2315	1.36764	0.683820	+	0.729651i	$0.260318\pi$
$242$	−31.3391	−2.01456
$243$	14.5197	0.931442
$244$	3.73230	0.238936
$245$	−3.19202	−0.203931
$246$	−18.6375	−1.18828
$247$	7.23567	0.460395
$248$	5.54987	0.352417
$249$	10.8902	0.690136
$250$	−11.5021	−0.727459
$251$	−14.0693	−0.888047	−0.444024	−	0.896015i	$-0.646449\pi$
$251$	−14.0693	−0.888047	−0.444024	+	0.896015i	$0.646449\pi$
$252$	15.0385	0.947335
$253$	14.2511	0.895957
$254$	19.6183	1.23096
$255$	−27.0062	−1.69120
$256$	1.00000	0.0625000
$257$	−17.5882	−1.09712	−0.548562	−	0.836110i	$-0.684824\pi$
$257$	−17.5882	−1.09712	−0.548562	+	0.836110i	$0.684824\pi$
$258$	−5.40050	−0.336220
$259$	14.7754	0.918099
$260$	6.49020	0.402505
$261$	−8.58748	−0.531551
$262$	−14.9845	−0.925746
$263$	19.4248	1.19778	0.598891	−	0.800830i	$-0.295608\pi$
$263$	19.4248	1.19778	0.598891	+	0.800830i	$0.295608\pi$
$264$	−18.3619	−1.13010
$265$	−2.37912	−0.146148
$266$	4.94522	0.303211
$267$	−49.8279	−3.04942
$268$	−14.0409	−0.857684
$269$	11.6592	0.710873	0.355437	−	0.934700i	$-0.384332\pi$
$269$	11.6592	0.710873	0.355437	+	0.934700i	$0.384332\pi$
$270$	−8.11104	−0.493622
$271$	−12.7256	−0.773025	−0.386512	−	0.922284i	$-0.626320\pi$
$271$	−12.7256	−0.773025	−0.386512	+	0.922284i	$0.626320\pi$
$272$	−6.53706	−0.396367
$273$	37.9054	2.29414
$274$	19.9718	1.20654
$275$	18.5886	1.12093
$276$	6.18050	0.372023
$277$	−12.1068	−0.727429	−0.363714	−	0.931511i	$-0.618492\pi$
$277$	−12.1068	−0.727429	−0.363714	+	0.931511i	$0.618492\pi$
$278$	−21.5488	−1.29241
$279$	−27.5459	−1.64913
$280$	4.43572	0.265085
$281$	23.7004	1.41385	0.706924	−	0.707290i	$-0.250082\pi$
$281$	23.7004	1.41385	0.706924	+	0.707290i	$0.250082\pi$
$282$	20.1412	1.19939
$283$	30.9156	1.83774	0.918870	−	0.394560i	$-0.129103\pi$
$283$	30.9156	1.83774	0.918870	+	0.394560i	$0.129103\pi$
$284$	−7.17329	−0.425656
$285$	−6.74275	−0.399406
$286$	−28.8466	−1.70574
$287$	−20.0110	−1.18121
$288$	−4.96334	−0.292467
$289$	25.7331	1.51371
$290$	−2.53295	−0.148740
$291$	−39.5351	−2.31759
$292$	−14.9201	−0.873131
$293$	18.0475	1.05434	0.527172	−	0.849758i	$-0.323252\pi$
$293$	18.0475	1.05434	0.527172	+	0.849758i	$0.323252\pi$
$294$	6.15288	0.358843
$295$	15.9771	0.930224
$296$	−4.87651	−0.283441
$297$	36.0507	2.09187
$298$	23.6769	1.37156
$299$	9.70957	0.561519
$300$	8.06163	0.465439
$301$	−5.79851	−0.334221
$302$	−9.82987	−0.565646
$303$	49.2504	2.82936
$304$	−1.63213	−0.0936091
$305$	−5.46400	−0.312868
$306$	32.4456	1.85479
$307$	14.2676	0.814298	0.407149	−	0.913362i	$-0.366523\pi$
$307$	14.2676	0.814298	0.407149	+	0.913362i	$0.366523\pi$
$308$	−19.7152	−1.12338
$309$	−24.2969	−1.38220
$310$	−8.12488	−0.461462
$311$	27.8016	1.57648	0.788242	−	0.615366i	$-0.210992\pi$
$311$	27.8016	1.57648	0.788242	+	0.615366i	$0.210992\pi$
$312$	−12.5104	−0.708262
$313$	−14.5793	−0.824070	−0.412035	−	0.911168i	$-0.635182\pi$
$313$	−14.5793	−0.824070	−0.412035	+	0.911168i	$0.635182\pi$
$314$	9.91111	0.559316
$315$	−22.0160	−1.24046
$316$	1.93882	0.109067
$317$	−10.6348	−0.597310	−0.298655	−	0.954361i	$-0.596538\pi$
$317$	−10.6348	−0.597310	−0.298655	+	0.954361i	$0.596538\pi$
$318$	4.58596	0.257168
$319$	11.2580	0.630329
$320$	−1.46398	−0.0818388
$321$	52.8923	2.95216
$322$	6.63600	0.369810
$323$	10.6693	0.593658
$324$	0.744700	0.0413722
$325$	12.6648	0.702518
$326$	11.5771	0.641195
$327$	37.7572	2.08798
$328$	6.60449	0.364672
$329$	21.6256	1.19226
$330$	26.8815	1.47978
$331$	−10.1390	−0.557289	−0.278644	−	0.960394i	$-0.589885\pi$
$331$	−10.1390	−0.557289	−0.278644	+	0.960394i	$0.589885\pi$
$332$	−3.85911	−0.211796
$333$	24.2038	1.32636
$334$	0.324636	0.0177633
$335$	20.5555	1.12307
$336$	−8.55023	−0.466453
$337$	−0.725346	−0.0395121	−0.0197561	−	0.999805i	$-0.506289\pi$
$337$	−0.725346	−0.0395121	−0.0197561	+	0.999805i	$0.506289\pi$
$338$	−6.65383	−0.361920
$339$	25.7507	1.39859
$340$	9.57010	0.519012
$341$	36.1122	1.95558
$342$	8.10082	0.438042
$343$	−14.6030	−0.788490
$344$	1.91376	0.103183
$345$	−9.04812	−0.487134
$346$	5.38821	0.289672
$347$	5.00784	0.268835	0.134418	−	0.990925i	$-0.457084\pi$
$347$	5.00784	0.268835	0.134418	+	0.990925i	$0.457084\pi$
$348$	4.88247	0.261728
$349$	−20.8257	−1.11477	−0.557387	−	0.830253i	$-0.688196\pi$
$349$	−20.8257	−1.11477	−0.557387	+	0.830253i	$0.688196\pi$
$350$	8.65577	0.462670
$351$	24.5621	1.31103
$352$	6.50685	0.346816
$353$	−7.66220	−0.407818	−0.203909	−	0.978990i	$-0.565365\pi$
$353$	−7.66220	−0.407818	−0.203909	+	0.978990i	$0.565365\pi$
$354$	−30.7973	−1.63686
$355$	10.5015	0.557363
$356$	17.6573	0.935836
$357$	55.8933	2.95819
$358$	−14.8329	−0.783942
$359$	0.236658	0.0124903	0.00624517	−	0.999980i	$-0.498012\pi$
$359$	0.236658	0.0124903	0.00624517	+	0.999980i	$0.498012\pi$
$360$	7.26621	0.382963
$361$	−16.3361	−0.859797
$362$	8.95412	0.470618
$363$	−88.4371	−4.64175
$364$	−13.4324	−0.704049
$365$	21.8426	1.14330
$366$	10.5323	0.550533
$367$	29.6537	1.54791	0.773954	−	0.633241i	$-0.218276\pi$
$367$	29.6537	1.54791	0.773954	+	0.633241i	$0.218276\pi$
$368$	−2.19016	−0.114170
$369$	−32.7803	−1.70648
$370$	7.13910	0.371144
$371$	4.92394	0.255638
$372$	15.6614	0.812005
$373$	−21.5425	−1.11543	−0.557715	−	0.830033i	$-0.688322\pi$
$373$	−21.5425	−1.11543	−0.557715	+	0.830033i	$0.688322\pi$
$374$	−42.5357	−2.19947
$375$	−32.4583	−1.67614
$376$	−7.13736	−0.368081
$377$	7.67035	0.395043
$378$	16.7870	0.863429
$379$	−1.63867	−0.0841728	−0.0420864	−	0.999114i	$-0.513400\pi$
$379$	−1.63867	−0.0841728	−0.0420864	+	0.999114i	$0.513400\pi$
$380$	2.38940	0.122574
$381$	55.3616	2.83626
$382$	−19.7490	−1.01045
$383$	−14.3630	−0.733914	−0.366957	−	0.930238i	$-0.619600\pi$
$383$	−14.3630	−0.733914	−0.366957	+	0.930238i	$0.619600\pi$
$384$	2.82194	0.144006
$385$	28.8626	1.47097
$386$	−5.61538	−0.285815
$387$	−9.49861	−0.482842
$388$	14.0099	0.711246
$389$	10.0688	0.510507	0.255253	−	0.966874i	$-0.417841\pi$
$389$	10.0688	0.510507	0.255253	+	0.966874i	$0.417841\pi$
$390$	18.3149	0.927413
$391$	14.3172	0.724053
$392$	−2.18037	−0.110126
$393$	−42.2853	−2.13301
$394$	15.3217	0.771894
$395$	−2.83839	−0.142815
$396$	−32.2957	−1.62292
$397$	15.5768	0.781777	0.390888	−	0.920438i	$-0.372168\pi$
$397$	15.5768	0.781777	0.390888	+	0.920438i	$0.372168\pi$
$398$	−2.13728	−0.107132
$399$	13.9551	0.698629
$400$	−2.85677	−0.142839
$401$	−25.0146	−1.24917	−0.624584	−	0.780957i	$-0.714732\pi$
$401$	−25.0146	−1.24917	−0.624584	+	0.780957i	$0.714732\pi$
$402$	−39.6225	−1.97619
$403$	24.6040	1.22561
$404$	−17.4527	−0.868303
$405$	−1.09022	−0.0541736
$406$	5.24230	0.260171
$407$	−31.7307	−1.57283
$408$	−18.4472	−0.913271
$409$	0.455269	0.0225116	0.0112558	−	0.999937i	$-0.496417\pi$
$409$	0.455269	0.0225116	0.0112558	+	0.999937i	$0.496417\pi$
$410$	−9.66883	−0.477509
$411$	56.3591	2.77999
$412$	8.61001	0.424185
$413$	−33.0670	−1.62712
$414$	10.8705	0.534257
$415$	5.64964	0.277330
$416$	4.43326	0.217359
$417$	−60.8094	−2.97785
$418$	−10.6200	−0.519443
$419$	−3.12795	−0.152810	−0.0764051	−	0.997077i	$-0.524344\pi$
$419$	−3.12795	−0.152810	−0.0764051	+	0.997077i	$0.524344\pi$
$420$	12.5173	0.610784
$421$	−11.3086	−0.551147	−0.275573	−	0.961280i	$-0.588868\pi$
$421$	−11.3086	−0.551147	−0.275573	+	0.961280i	$0.588868\pi$
$422$	−9.11310	−0.443619
$423$	35.4251	1.72243
$424$	−1.62511	−0.0789223
$425$	18.6749	0.905865
$426$	−20.2426	−0.980756
$427$	11.3086	0.547259
$428$	−18.7433	−0.905990
$429$	−81.4033	−3.93019
$430$	−2.80169	−0.135110
$431$	−17.3422	−0.835346	−0.417673	−	0.908597i	$-0.637154\pi$
$431$	−17.3422	−0.835346	−0.417673	+	0.908597i	$0.637154\pi$
$432$	−5.54041	−0.266563
$433$	23.7963	1.14358	0.571789	−	0.820400i	$-0.306249\pi$
$433$	23.7963	1.14358	0.571789	+	0.820400i	$0.306249\pi$
$434$	16.8156	0.807175
$435$	−7.14782	−0.342712
$436$	−13.3799	−0.640780
$437$	3.57463	0.170998
$438$	−42.1035	−2.01178
$439$	1.12925	0.0538962	0.0269481	−	0.999637i	$-0.491421\pi$
$439$	1.12925	0.0538962	0.0269481	+	0.999637i	$0.491421\pi$
$440$	−9.52588	−0.454129
$441$	10.8219	0.515330
$442$	−28.9805	−1.37846
$443$	2.94603	0.139970	0.0699852	−	0.997548i	$-0.477705\pi$
$443$	2.94603	0.139970	0.0699852	+	0.997548i	$0.477705\pi$
$444$	−13.7612	−0.653078
$445$	−25.8499	−1.22540
$446$	−2.83838	−0.134401
$447$	66.8146	3.16022
$448$	3.02991	0.143150
$449$	18.2475	0.861151	0.430576	−	0.902554i	$-0.358311\pi$
$449$	18.2475	0.861151	0.430576	+	0.902554i	$0.358311\pi$
$450$	14.1791	0.668410
$451$	42.9745	2.02359
$452$	−9.12519	−0.429213
$453$	−27.7393	−1.30331
$454$	12.8931	0.605102
$455$	19.6647	0.921897
$456$	−4.60577	−0.215685
$457$	−30.3549	−1.41994	−0.709970	−	0.704232i	$-0.751292\pi$
$457$	−30.3549	−1.41994	−0.709970	+	0.704232i	$0.751292\pi$
$458$	4.75894	0.222371
$459$	36.2180	1.69051
$460$	3.20635	0.149497
$461$	15.2365	0.709633	0.354817	−	0.934936i	$-0.384543\pi$
$461$	15.2365	0.709633	0.354817	+	0.934936i	$0.384543\pi$
$462$	−55.6351	−2.58838
$463$	34.5415	1.60528	0.802641	−	0.596463i	$-0.203428\pi$
$463$	34.5415	1.60528	0.802641	+	0.596463i	$0.203428\pi$
$464$	−1.73018	−0.0803217
$465$	−22.9279	−1.06326
$466$	24.6821	1.14338
$467$	−3.04551	−0.140929	−0.0704647	−	0.997514i	$-0.522448\pi$
$467$	−3.04551	−0.140929	−0.0704647	+	0.997514i	$0.522448\pi$
$468$	−22.0038	−1.01713
$469$	−42.5427	−1.96444
$470$	10.4489	0.481973
$471$	27.9685	1.28872
$472$	10.9135	0.502335
$473$	12.4525	0.572568
$474$	5.47124	0.251303
$475$	4.66263	0.213936
$476$	−19.8067	−0.907839
$477$	8.06597	0.369315
$478$	−4.15919	−0.190237
$479$	−38.6905	−1.76781	−0.883907	−	0.467663i	$-0.845096\pi$
$479$	−38.6905	−1.76781	−0.883907	+	0.467663i	$0.845096\pi$
$480$	−4.13125	−0.188565
$481$	−21.6188	−0.985735
$482$	−21.2315	−0.967067
$483$	18.7264	0.852080
$484$	31.3391	1.42451
$485$	−20.5102	−0.931321
$486$	−14.5197	−0.658629
$487$	−4.11267	−0.186363	−0.0931814	−	0.995649i	$-0.529704\pi$
$487$	−4.11267	−0.186363	−0.0931814	+	0.995649i	$0.529704\pi$
$488$	−3.73230	−0.168953
$489$	32.6698	1.47738
$490$	3.19202	0.144201
$491$	14.2410	0.642688	0.321344	−	0.946963i	$-0.395865\pi$
$491$	14.2410	0.642688	0.321344	+	0.946963i	$0.395865\pi$
$492$	18.6375	0.840242
$493$	11.3103	0.509390
$494$	−7.23567	−0.325548
$495$	47.2802	2.12509
$496$	−5.54987	−0.249196
$497$	−21.7344	−0.974923
$498$	−10.8902	−0.488000
$499$	−8.77860	−0.392984	−0.196492	−	0.980505i	$-0.562955\pi$
$499$	−8.77860	−0.392984	−0.196492	+	0.980505i	$0.562955\pi$
$500$	11.5021	0.514391
$501$	0.916103	0.0409285
$502$	14.0693	0.627944
$503$	−13.7681	−0.613891	−0.306946	−	0.951727i	$-0.599307\pi$
$503$	−13.7681	−0.613891	−0.306946	+	0.951727i	$0.599307\pi$
$504$	−15.0385	−0.669867
$505$	25.5503	1.13697
$506$	−14.2511	−0.633537
$507$	−18.7767	−0.833902
$508$	−19.6183	−0.870420
$509$	−28.3985	−1.25874	−0.629371	−	0.777105i	$-0.716688\pi$
$509$	−28.3985	−1.25874	−0.629371	+	0.777105i	$0.716688\pi$
$510$	27.0062	1.19586
$511$	−45.2065	−1.99982
$512$	−1.00000	−0.0441942
$513$	9.04268	0.399244
$514$	17.5882	0.775783
$515$	−12.6048	−0.555436
$516$	5.40050	0.237744
$517$	−46.4417	−2.04251
$518$	−14.7754	−0.649194
$519$	15.2052	0.667434
$520$	−6.49020	−0.284614
$521$	−25.1560	−1.10211	−0.551053	−	0.834470i	$-0.685774\pi$
$521$	−25.1560	−1.10211	−0.551053	+	0.834470i	$0.685774\pi$
$522$	8.58748	0.375864
$523$	−14.5445	−0.635987	−0.317993	−	0.948093i	$-0.603009\pi$
$523$	−14.5445	−0.635987	−0.317993	+	0.948093i	$0.603009\pi$
$524$	14.9845	0.654601
$525$	24.4261	1.06604
$526$	−19.4248	−0.846960
$527$	36.2798	1.58037
$528$	18.3619	0.799101
$529$	−18.2032	−0.791443
$530$	2.37912	0.103342
$531$	−54.1674	−2.35067
$532$	−4.94522	−0.214402
$533$	29.2795	1.26823
$534$	49.8279	2.15626
$535$	27.4397	1.18632
$536$	14.0409	0.606474
$537$	−41.8575	−1.80628
$538$	−11.6592	−0.502663
$539$	−14.1874	−0.611094
$540$	8.11104	0.349044
$541$	8.27359	0.355709	0.177855	−	0.984057i	$-0.443084\pi$
$541$	8.27359	0.355709	0.177855	+	0.984057i	$0.443084\pi$
$542$	12.7256	0.546611
$543$	25.2680	1.08435
$544$	6.53706	0.280274
$545$	19.5878	0.839051
$546$	−37.9054	−1.62220
$547$	−23.8217	−1.01854	−0.509271	−	0.860606i	$-0.670085\pi$
$547$	−23.8217	−1.01854	−0.509271	+	0.860606i	$0.670085\pi$
$548$	−19.9718	−0.853152
$549$	18.5247	0.790614
$550$	−18.5886	−0.792620
$551$	2.82388	0.120302
$552$	−6.18050	−0.263060
$553$	5.87447	0.249808
$554$	12.1068	0.514370
$555$	20.1461	0.855154
$556$	21.5488	0.913873
$557$	−24.3767	−1.03287	−0.516436	−	0.856326i	$-0.672742\pi$
$557$	−24.3767	−1.03287	−0.516436	+	0.856326i	$0.672742\pi$
$558$	27.5459	1.16611
$559$	8.48418	0.358843
$560$	−4.43572	−0.187444
$561$	−120.033	−5.06780
$562$	−23.7004	−0.999741
$563$	9.84571	0.414947	0.207474	−	0.978241i	$-0.433476\pi$
$563$	9.84571	0.414947	0.207474	+	0.978241i	$0.433476\pi$
$564$	−20.1412	−0.848097
$565$	13.3591	0.562020
$566$	−30.9156	−1.29948
$567$	2.25638	0.0947589
$568$	7.17329	0.300984
$569$	−2.95663	−0.123948	−0.0619741	−	0.998078i	$-0.519740\pi$
$569$	−2.95663	−0.123948	−0.0619741	+	0.998078i	$0.519740\pi$
$570$	6.74275	0.282423
$571$	−28.3270	−1.18545	−0.592723	−	0.805406i	$-0.701947\pi$
$571$	−28.3270	−1.18545	−0.592723	+	0.805406i	$0.701947\pi$
$572$	28.8466	1.20614
$573$	−55.7305	−2.32817
$574$	20.0110	0.835245
$575$	6.25679	0.260926
$576$	4.96334	0.206806
$577$	−19.7791	−0.823415	−0.411708	−	0.911316i	$-0.635067\pi$
$577$	−19.7791	−0.823415	−0.411708	+	0.911316i	$0.635067\pi$
$578$	−25.7331	−1.07036
$579$	−15.8462	−0.658548
$580$	2.53295	0.105175
$581$	−11.6928	−0.485097
$582$	39.5351	1.63878
$583$	−10.5743	−0.437945
$584$	14.9201	0.617397
$585$	32.2130	1.33184
$586$	−18.0475	−0.745534
$587$	40.1016	1.65517	0.827585	−	0.561341i	$-0.189714\pi$
$587$	40.1016	1.65517	0.827585	+	0.561341i	$0.189714\pi$
$588$	−6.15288	−0.253741
$589$	9.05811	0.373233
$590$	−15.9771	−0.657768
$591$	43.2368	1.77852
$592$	4.87651	0.200423
$593$	31.0164	1.27369	0.636845	−	0.770992i	$-0.280239\pi$
$593$	31.0164	1.27369	0.636845	+	0.770992i	$0.280239\pi$
$594$	−36.0507	−1.47918
$595$	28.9966	1.18874
$596$	−23.6769	−0.969842
$597$	−6.03128	−0.246844
$598$	−9.70957	−0.397054
$599$	−10.3984	−0.424868	−0.212434	−	0.977175i	$-0.568139\pi$
$599$	−10.3984	−0.424868	−0.212434	+	0.977175i	$0.568139\pi$
$600$	−8.06163	−0.329115
$601$	42.9806	1.75321	0.876607	−	0.481207i	$-0.159802\pi$
$601$	42.9806	1.75321	0.876607	+	0.481207i	$0.159802\pi$
$602$	5.79851	0.236330
$603$	−69.6897	−2.83798
$604$	9.82987	0.399972
$605$	−45.8798	−1.86528
$606$	−49.2504	−2.00066
$607$	33.3003	1.35162	0.675808	−	0.737078i	$-0.263795\pi$
$607$	33.3003	1.35162	0.675808	+	0.737078i	$0.263795\pi$
$608$	1.63213	0.0661917
$609$	14.7935	0.599461
$610$	5.46400	0.221231
$611$	−31.6418	−1.28009
$612$	−32.4456	−1.31154
$613$	2.63315	0.106352	0.0531759	−	0.998585i	$-0.483066\pi$
$613$	2.63315	0.106352	0.0531759	+	0.998585i	$0.483066\pi$
$614$	−14.2676	−0.575795
$615$	−27.2848	−1.10023
$616$	19.7152	0.794348
$617$	35.6454	1.43503	0.717516	−	0.696542i	$-0.245279\pi$
$617$	35.6454	1.43503	0.717516	+	0.696542i	$0.245279\pi$
$618$	24.2969	0.977365
$619$	33.9716	1.36544	0.682718	−	0.730682i	$-0.260798\pi$
$619$	33.9716	1.36544	0.682718	+	0.730682i	$0.260798\pi$
$620$	8.12488	0.326303
$621$	12.1344	0.486937
$622$	−27.8016	−1.11474
$623$	53.5001	2.14344
$624$	12.5104	0.500817
$625$	−2.55500	−0.102200
$626$	14.5793	0.582706
$627$	−29.9691	−1.19685
$628$	−9.91111	−0.395496
$629$	−31.8780	−1.27106
$630$	22.0160	0.877138
$631$	32.0822	1.27717	0.638586	−	0.769550i	$-0.279520\pi$
$631$	32.0822	1.27717	0.638586	+	0.769550i	$0.279520\pi$
$632$	−1.93882	−0.0771223
$633$	−25.7166	−1.02214
$634$	10.6348	0.422362
$635$	28.7207	1.13975
$636$	−4.58596	−0.181845
$637$	−9.66618	−0.382988
$638$	−11.2580	−0.445710
$639$	−35.6034	−1.40845
$640$	1.46398	0.0578688
$641$	43.3843	1.71358	0.856788	−	0.515668i	$-0.172456\pi$
$641$	43.3843	1.71358	0.856788	+	0.515668i	$0.172456\pi$
$642$	−52.8923	−2.08749
$643$	−37.9867	−1.49805	−0.749026	−	0.662541i	$-0.769478\pi$
$643$	−37.9867	−1.49805	−0.749026	+	0.662541i	$0.769478\pi$
$644$	−6.63600	−0.261495
$645$	−7.90621	−0.311307
$646$	−10.6693	−0.419779
$647$	20.3732	0.800953	0.400477	−	0.916307i	$-0.368845\pi$
$647$	20.3732	0.800953	0.400477	+	0.916307i	$0.368845\pi$
$648$	−0.744700	−0.0292546
$649$	71.0126	2.78749
$650$	−12.6648	−0.496755
$651$	47.4526	1.85982
$652$	−11.5771	−0.453393
$653$	43.5596	1.70462	0.852310	−	0.523036i	$-0.175201\pi$
$653$	43.5596	1.70462	0.852310	+	0.523036i	$0.175201\pi$
$654$	−37.7572	−1.47642
$655$	−21.9370	−0.857148
$656$	−6.60449	−0.257862
$657$	−74.0533	−2.88910
$658$	−21.6256	−0.843052
$659$	13.1273	0.511369	0.255684	−	0.966760i	$-0.417699\pi$
$659$	13.1273	0.511369	0.255684	+	0.966760i	$0.417699\pi$
$660$	−26.8815	−1.04636
$661$	1.46238	0.0568799	0.0284400	−	0.999596i	$-0.490946\pi$
$661$	1.46238	0.0568799	0.0284400	+	0.999596i	$0.490946\pi$
$662$	10.1390	0.394063
$663$	−81.7812	−3.17612
$664$	3.85911	0.149762
$665$	7.23968	0.280743
$666$	−24.2038	−0.937876
$667$	3.78938	0.146725
$668$	−0.324636	−0.0125606
$669$	−8.00973	−0.309674
$670$	−20.5555	−0.794130
$671$	−24.2855	−0.937533
$672$	8.55023	0.329832
$673$	−14.6230	−0.563675	−0.281837	−	0.959462i	$-0.590944\pi$
$673$	−14.6230	−0.563675	−0.281837	+	0.959462i	$0.590944\pi$
$674$	0.725346	0.0279393
$675$	15.8277	0.609208
$676$	6.65383	0.255916
$677$	−42.6209	−1.63805	−0.819026	−	0.573756i	$-0.805486\pi$
$677$	−42.6209	−1.63805	−0.819026	+	0.573756i	$0.805486\pi$
$678$	−25.7507	−0.988950
$679$	42.4489	1.62904
$680$	−9.57010	−0.366997
$681$	36.3835	1.39422
$682$	−36.1122	−1.38281
$683$	−2.62888	−0.100591	−0.0502957	−	0.998734i	$-0.516016\pi$
$683$	−2.62888	−0.100591	−0.0502957	+	0.998734i	$0.516016\pi$
$684$	−8.10082	−0.309742
$685$	29.2382	1.11714
$686$	14.6030	0.557547
$687$	13.4294	0.512365
$688$	−1.91376	−0.0729613
$689$	−7.20454	−0.274471
$690$	9.04812	0.344456
$691$	−8.97368	−0.341375	−0.170687	−	0.985325i	$-0.554599\pi$
$691$	−8.97368	−0.341375	−0.170687	+	0.985325i	$0.554599\pi$
$692$	−5.38821	−0.204829
$693$	−97.8532	−3.71714
$694$	−5.00784	−0.190095
$695$	−31.5470	−1.19664
$696$	−4.88247	−0.185069
$697$	43.1740	1.63533
$698$	20.8257	0.788264
$699$	69.6515	2.63446
$700$	−8.65577	−0.327157
$701$	9.80744	0.370422	0.185211	−	0.982699i	$-0.440703\pi$
$701$	9.80744	0.370422	0.185211	+	0.982699i	$0.440703\pi$
$702$	−24.5621	−0.927037
$703$	−7.95910	−0.300183
$704$	−6.50685	−0.245236
$705$	29.4862	1.11052
$706$	7.66220	0.288371
$707$	−52.8801	−1.98876
$708$	30.7973	1.15743
$709$	34.8451	1.30864	0.654318	−	0.756219i	$-0.272956\pi$
$709$	34.8451	1.30864	0.654318	+	0.756219i	$0.272956\pi$
$710$	−10.5015	−0.394115
$711$	9.62304	0.360892
$712$	−17.6573	−0.661736
$713$	12.1551	0.455213
$714$	−55.8933	−2.09176
$715$	−42.2308	−1.57934
$716$	14.8329	0.554331
$717$	−11.7370	−0.438325
$718$	−0.236658	−0.00883200
$719$	−5.44164	−0.202939	−0.101469	−	0.994839i	$-0.532354\pi$
$719$	−5.44164	−0.202939	−0.101469	+	0.994839i	$0.532354\pi$
$720$	−7.26621	−0.270796
$721$	26.0876	0.971552
$722$	16.3361	0.607968
$723$	−59.9139	−2.22822
$724$	−8.95412	−0.332777
$725$	4.94274	0.183569
$726$	88.4371	3.28221
$727$	−29.1055	−1.07946	−0.539732	−	0.841837i	$-0.681474\pi$
$727$	−29.1055	−1.07946	−0.539732	+	0.841837i	$0.681474\pi$
$728$	13.4324	0.497838
$729$	−43.2079	−1.60029
$730$	−21.8426	−0.808432
$731$	12.5103	0.462711
$732$	−10.5323	−0.389286
$733$	−23.7742	−0.878121	−0.439061	−	0.898457i	$-0.644689\pi$
$733$	−23.7742	−0.878121	−0.439061	+	0.898457i	$0.644689\pi$
$734$	−29.6537	−1.09454
$735$	9.00768	0.332253
$736$	2.19016	0.0807305
$737$	91.3621	3.36537
$738$	32.7803	1.20666
$739$	−10.0885	−0.371112	−0.185556	−	0.982634i	$-0.559409\pi$
$739$	−10.0885	−0.371112	−0.185556	+	0.982634i	$0.559409\pi$
$740$	−7.13910	−0.262438
$741$	−20.4186	−0.750096
$742$	−4.92394	−0.180764
$743$	6.05747	0.222227	0.111113	−	0.993808i	$-0.464558\pi$
$743$	6.05747	0.222227	0.111113	+	0.993808i	$0.464558\pi$
$744$	−15.6614	−0.574174
$745$	34.6624	1.26993
$746$	21.5425	0.788728
$747$	−19.1540	−0.700810
$748$	42.5357	1.55526
$749$	−56.7905	−2.07508
$750$	32.4583	1.18521
$751$	−0.00557344	−0.000203378 0	−0.000101689	−	1.00000i	$-0.500032\pi$
$751$	−0.00557344	−0.000203378 0	−0.000101689		1.00000i	$0.500032\pi$
$752$	7.13736	0.260273
$753$	39.7027	1.44685
$754$	−7.67035	−0.279338
$755$	−14.3907	−0.523731
$756$	−16.7870	−0.610536
$757$	−48.1829	−1.75124	−0.875620	−	0.483001i	$-0.839547\pi$
$757$	−48.1829	−1.75124	−0.875620	+	0.483001i	$0.839547\pi$
$758$	1.63867	0.0595192
$759$	−40.2156	−1.45974
$760$	−2.38940	−0.0866727
$761$	27.1909	0.985671	0.492835	−	0.870123i	$-0.335960\pi$
$761$	27.1909	0.985671	0.492835	+	0.870123i	$0.335960\pi$
$762$	−55.3616	−2.00554
$763$	−40.5399	−1.46764
$764$	19.7490	0.714494
$765$	47.4996	1.71735
$766$	14.3630	0.518955
$767$	48.3825	1.74699
$768$	−2.82194	−0.101828
$769$	−2.59541	−0.0935928	−0.0467964	−	0.998904i	$-0.514901\pi$
$769$	−2.59541	−0.0935928	−0.0467964	+	0.998904i	$0.514901\pi$
$770$	−28.8626	−1.04014
$771$	49.6329	1.78748
$772$	5.61538	0.202102
$773$	10.5331	0.378849	0.189424	−	0.981895i	$-0.439338\pi$
$773$	10.5331	0.378849	0.189424	+	0.981895i	$0.439338\pi$
$774$	9.49861	0.341421
$775$	15.8547	0.569518
$776$	−14.0099	−0.502927
$777$	−41.6953	−1.49581
$778$	−10.0688	−0.360983
$779$	10.7794	0.386212
$780$	−18.3149	−0.655780
$781$	46.6755	1.67018
$782$	−14.3172	−0.511983
$783$	9.58593	0.342573
$784$	2.18037	0.0778705
$785$	14.5096	0.517871
$786$	42.2853	1.50827
$787$	−5.41002	−0.192846	−0.0964232	−	0.995340i	$-0.530740\pi$
$787$	−5.41002	−0.192846	−0.0964232	+	0.995340i	$0.530740\pi$
$788$	−15.3217	−0.545811
$789$	−54.8155	−1.95148
$790$	2.83839	0.100986
$791$	−27.6485	−0.983068
$792$	32.2957	1.14758
$793$	−16.5463	−0.587576
$794$	−15.5768	−0.552799
$795$	6.71374	0.238112
$796$	2.13728	0.0757540
$797$	27.6755	0.980315	0.490158	−	0.871634i	$-0.336939\pi$
$797$	27.6755	0.980315	0.490158	+	0.871634i	$0.336939\pi$
$798$	−13.9551	−0.494005
$799$	−46.6573	−1.65062
$800$	2.85677	0.101002
$801$	87.6392	3.09658
$802$	25.0146	0.883296
$803$	97.0827	3.42597
$804$	39.6225	1.39738
$805$	9.71496	0.342407
$806$	−24.6040	−0.866640
$807$	−32.9015	−1.15819
$808$	17.4527	0.613983
$809$	2.24454	0.0789137	0.0394569	−	0.999221i	$-0.487437\pi$
$809$	2.24454	0.0789137	0.0394569	+	0.999221i	$0.487437\pi$
$810$	1.09022	0.0383065
$811$	40.3802	1.41794	0.708970	−	0.705239i	$-0.249160\pi$
$811$	40.3802	1.41794	0.708970	+	0.705239i	$0.249160\pi$
$812$	−5.24230	−0.183969
$813$	35.9108	1.25945
$814$	31.7307	1.11216
$815$	16.9486	0.593683
$816$	18.4472	0.645780
$817$	3.12350	0.109277
$818$	−0.455269	−0.0159181
$819$	−66.6695	−2.32962
$820$	9.66883	0.337650
$821$	−4.76420	−0.166272	−0.0831359	−	0.996538i	$-0.526494\pi$
$821$	−4.76420	−0.166272	−0.0831359	+	0.996538i	$0.526494\pi$
$822$	−56.3591	−1.96575
$823$	−17.5536	−0.611878	−0.305939	−	0.952051i	$-0.598970\pi$
$823$	−17.5536	−0.611878	−0.305939	+	0.952051i	$0.598970\pi$
$824$	−8.61001	−0.299944
$825$	−52.4559	−1.82628
$826$	33.0670	1.15055
$827$	−0.515239	−0.0179166	−0.00895830	−	0.999960i	$-0.502852\pi$
$827$	−0.515239	−0.0179166	−0.00895830	+	0.999960i	$0.502852\pi$
$828$	−10.8705	−0.377776
$829$	5.53341	0.192183	0.0960916	−	0.995373i	$-0.469366\pi$
$829$	5.53341	0.192183	0.0960916	+	0.995373i	$0.469366\pi$
$830$	−5.64964	−0.196102
$831$	34.1647	1.18516
$832$	−4.43326	−0.153696
$833$	−14.2532	−0.493845
$834$	60.8094	2.10566
$835$	0.475260	0.0164470
$836$	10.6200	0.367302
$837$	30.7486	1.06283
$838$	3.12795	0.108053
$839$	39.2550	1.35523	0.677617	−	0.735415i	$-0.263013\pi$
$839$	39.2550	1.35523	0.677617	+	0.735415i	$0.263013\pi$
$840$	−12.5173	−0.431889
$841$	−26.0065	−0.896775
$842$	11.3086	0.389719
$843$	−66.8811	−2.30351
$844$	9.11310	0.313686
$845$	−9.74105	−0.335102
$846$	−35.4251	−1.21794
$847$	94.9549	3.26269
$848$	1.62511	0.0558065
$849$	−87.2419	−2.99413
$850$	−18.6749	−0.640543
$851$	−10.6803	−0.366118
$852$	20.2426	0.693499
$853$	−55.4202	−1.89755	−0.948776	−	0.315950i	$-0.897677\pi$
$853$	−55.4202	−1.89755	−0.948776	+	0.315950i	$0.897677\pi$
$854$	−11.3086	−0.386971
$855$	11.8594	0.405583
$856$	18.7433	0.640631
$857$	−15.8070	−0.539958	−0.269979	−	0.962866i	$-0.587017\pi$
$857$	−15.8070	−0.539958	−0.269979	+	0.962866i	$0.587017\pi$
$858$	81.4033	2.77906
$859$	24.9610	0.851659	0.425829	−	0.904804i	$-0.359982\pi$
$859$	24.9610	0.851659	0.425829	+	0.904804i	$0.359982\pi$
$860$	2.80169	0.0955370
$861$	56.4699	1.92449
$862$	17.3422	0.590679
$863$	27.8446	0.947841	0.473921	−	0.880568i	$-0.342838\pi$
$863$	27.8446	0.947841	0.473921	+	0.880568i	$0.342838\pi$
$864$	5.54041	0.188489
$865$	7.88821	0.268207
$866$	−23.7963	−0.808632
$867$	−72.6172	−2.46621
$868$	−16.8156	−0.570759
$869$	−12.6156	−0.427957
$870$	7.14782	0.242334
$871$	62.2470	2.10916
$872$	13.3799	0.453100
$873$	69.5360	2.35344
$874$	−3.57463	−0.120914
$875$	34.8505	1.17816
$876$	42.1035	1.42255
$877$	−34.6702	−1.17073	−0.585365	−	0.810770i	$-0.699049\pi$
$877$	−34.6702	−1.17073	−0.585365	+	0.810770i	$0.699049\pi$
$878$	−1.12925	−0.0381104
$879$	−50.9289	−1.71779
$880$	9.52588	0.321117
$881$	−13.7252	−0.462415	−0.231208	−	0.972904i	$-0.574268\pi$
$881$	−13.7252	−0.462415	−0.231208	+	0.972904i	$0.574268\pi$
$882$	−10.8219	−0.364393
$883$	17.1895	0.578472	0.289236	−	0.957258i	$-0.406599\pi$
$883$	17.1895	0.578472	0.289236	+	0.957258i	$0.406599\pi$
$884$	28.9805	0.974720
$885$	−45.0865	−1.51557
$886$	−2.94603	−0.0989740
$887$	−37.9003	−1.27257	−0.636284	−	0.771455i	$-0.719529\pi$
$887$	−37.9003	−1.27257	−0.636284	+	0.771455i	$0.719529\pi$
$888$	13.7612	0.461796
$889$	−59.4417	−1.99361
$890$	25.8499	0.866491
$891$	−4.84565	−0.162335
$892$	2.83838	0.0950359
$893$	−11.6491	−0.389822
$894$	−66.8146	−2.23462
$895$	−21.7150	−0.725852
$896$	−3.02991	−0.101222
$897$	−27.3998	−0.914853
$898$	−18.2475	−0.608926
$899$	9.60228	0.320254
$900$	−14.1791	−0.472637
$901$	−10.6234	−0.353918
$902$	−42.9745	−1.43089
$903$	16.3630	0.544528
$904$	9.12519	0.303499
$905$	13.1086	0.435746
$906$	27.7393	0.921577
$907$	21.7126	0.720954	0.360477	−	0.932768i	$-0.382614\pi$
$907$	21.7126	0.720954	0.360477	+	0.932768i	$0.382614\pi$
$908$	−12.8931	−0.427872
$909$	−86.6235	−2.87312
$910$	−19.6647	−0.651879
$911$	−20.1146	−0.666427	−0.333214	−	0.942851i	$-0.608133\pi$
$911$	−20.1146	−0.666427	−0.333214	+	0.942851i	$0.608133\pi$
$912$	4.60577	0.152512
$913$	25.1106	0.831041
$914$	30.3549	1.00405
$915$	15.4191	0.509739
$916$	−4.75894	−0.157240
$917$	45.4018	1.49930
$918$	−36.2180	−1.19537
$919$	−39.0670	−1.28870	−0.644350	−	0.764730i	$-0.722872\pi$
$919$	−39.0670	−1.28870	−0.644350	+	0.764730i	$0.722872\pi$
$920$	−3.20635	−0.105710
$921$	−40.2624	−1.32669
$922$	−15.2365	−0.501786
$923$	31.8011	1.04674
$924$	55.6351	1.83026
$925$	−13.9311	−0.458051
$926$	−34.5415	−1.13511
$927$	42.7344	1.40358
$928$	1.73018	0.0567960
$929$	−38.3293	−1.25754	−0.628772	−	0.777590i	$-0.716442\pi$
$929$	−38.3293	−1.25754	−0.628772	+	0.777590i	$0.716442\pi$
$930$	22.9279	0.751836
$931$	−3.55866	−0.116630
$932$	−24.6821	−0.808490
$933$	−78.4544	−2.56848
$934$	3.04551	0.0996522
$935$	−62.2712	−2.03649
$936$	22.0038	0.719216
$937$	−45.0104	−1.47043	−0.735213	−	0.677836i	$-0.762918\pi$
$937$	−45.0104	−1.47043	−0.735213	+	0.677836i	$0.762918\pi$
$938$	42.5427	1.38907
$939$	41.1419	1.34261
$940$	−10.4489	−0.340806
$941$	11.5345	0.376015	0.188007	−	0.982168i	$-0.439797\pi$
$941$	11.5345	0.376015	0.188007	+	0.982168i	$0.439797\pi$
$942$	−27.9685	−0.911265
$943$	14.4649	0.471042
$944$	−10.9135	−0.355205
$945$	24.5757	0.799449
$946$	−12.4525	−0.404867
$947$	−4.38393	−0.142458	−0.0712292	−	0.997460i	$-0.522692\pi$
$947$	−4.38393	−0.142458	−0.0712292	+	0.997460i	$0.522692\pi$
$948$	−5.47124	−0.177698
$949$	66.1446	2.14714
$950$	−4.66263	−0.151276
$951$	30.0108	0.973165
$952$	19.8067	0.641939
$953$	−1.59541	−0.0516804	−0.0258402	−	0.999666i	$-0.508226\pi$
$953$	−1.59541	−0.0516804	−0.0258402	+	0.999666i	$0.508226\pi$
$954$	−8.06597	−0.261145
$955$	−28.9121	−0.935573
$956$	4.15919	0.134518
$957$	−31.7695	−1.02696
$958$	38.6905	1.25003
$959$	−60.5128	−1.95406
$960$	4.13125	0.133336
$961$	−0.198974	−0.00641851
$962$	21.6188	0.697020
$963$	−93.0291	−2.99782
$964$	21.2315	0.683820
$965$	−8.22078	−0.264636
$966$	−18.7264	−0.602512
$967$	−30.4189	−0.978205	−0.489102	−	0.872226i	$-0.662676\pi$
$967$	−30.4189	−0.978205	−0.489102	+	0.872226i	$0.662676\pi$
$968$	−31.3391	−1.00728
$969$	−30.1082	−0.967215
$970$	20.5102	0.658543
$971$	7.67415	0.246275	0.123138	−	0.992390i	$-0.460704\pi$
$971$	7.67415	0.246275	0.123138	+	0.992390i	$0.460704\pi$
$972$	14.5197	0.465721
$973$	65.2910	2.09313
$974$	4.11267	0.131778
$975$	−35.7393	−1.14458
$976$	3.73230	0.119468
$977$	−16.2904	−0.521177	−0.260589	−	0.965450i	$-0.583917\pi$
$977$	−16.2904	−0.521177	−0.260589	+	0.965450i	$0.583917\pi$
$978$	−32.6698	−1.04466
$979$	−114.894	−3.67201
$980$	−3.19202	−0.101965
$981$	−66.4089	−2.12027
$982$	−14.2410	−0.454449
$983$	−60.3337	−1.92434	−0.962172	−	0.272441i	$-0.912169\pi$
$983$	−60.3337	−1.92434	−0.962172	+	0.272441i	$0.912169\pi$
$984$	−18.6375	−0.594141
$985$	22.4305	0.714697
$986$	−11.3103	−0.360193
$987$	−61.0260	−1.94248
$988$	7.23567	0.230197
$989$	4.19144	0.133280
$990$	−47.2802	−1.50266
$991$	−41.1911	−1.30848	−0.654240	−	0.756287i	$-0.727011\pi$
$991$	−41.1911	−1.30848	−0.654240	+	0.756287i	$0.727011\pi$
$992$	5.54987	0.176208
$993$	28.6116	0.907961
$994$	21.7344	0.689374
$995$	−3.12893	−0.0991939
$996$	10.8902	0.345068
$997$	−24.8164	−0.785943	−0.392971	−	0.919551i	$-0.628553\pi$
$997$	−24.8164	−0.785943	−0.392971	+	0.919551i	$0.628553\pi$
$998$	8.77860	0.277882
$999$	−27.0179	−0.854808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.3	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.3	✓	49	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.82194 q^{3} +1.00000 q^{4} -1.46398 q^{5} +2.82194 q^{6} +3.02991 q^{7} -1.00000 q^{8} +4.96334 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.82194 q^{3} +1.00000 q^{4} -1.46398 q^{5} +2.82194 q^{6} +3.02991 q^{7} -1.00000 q^{8} +4.96334 q^{9} +1.46398 q^{10} -6.50685 q^{11} -2.82194 q^{12} -4.43326 q^{13} -3.02991 q^{14} +4.13125 q^{15} +1.00000 q^{16} -6.53706 q^{17} -4.96334 q^{18} -1.63213 q^{19} -1.46398 q^{20} -8.55023 q^{21} +6.50685 q^{22} -2.19016 q^{23} +2.82194 q^{24} -2.85677 q^{25} +4.43326 q^{26} -5.54041 q^{27} +3.02991 q^{28} -1.73018 q^{29} -4.13125 q^{30} -5.54987 q^{31} -1.00000 q^{32} +18.3619 q^{33} +6.53706 q^{34} -4.43572 q^{35} +4.96334 q^{36} +4.87651 q^{37} +1.63213 q^{38} +12.5104 q^{39} +1.46398 q^{40} -6.60449 q^{41} +8.55023 q^{42} -1.91376 q^{43} -6.50685 q^{44} -7.26621 q^{45} +2.19016 q^{46} +7.13736 q^{47} -2.82194 q^{48} +2.18037 q^{49} +2.85677 q^{50} +18.4472 q^{51} -4.43326 q^{52} +1.62511 q^{53} +5.54041 q^{54} +9.52588 q^{55} -3.02991 q^{56} +4.60577 q^{57} +1.73018 q^{58} -10.9135 q^{59} +4.13125 q^{60} +3.73230 q^{61} +5.54987 q^{62} +15.0385 q^{63} +1.00000 q^{64} +6.49020 q^{65} -18.3619 q^{66} -14.0409 q^{67} -6.53706 q^{68} +6.18050 q^{69} +4.43572 q^{70} -7.17329 q^{71} -4.96334 q^{72} -14.9201 q^{73} -4.87651 q^{74} +8.06163 q^{75} -1.63213 q^{76} -19.7152 q^{77} -12.5104 q^{78} +1.93882 q^{79} -1.46398 q^{80} +0.744700 q^{81} +6.60449 q^{82} -3.85911 q^{83} -8.55023 q^{84} +9.57010 q^{85} +1.91376 q^{86} +4.88247 q^{87} +6.50685 q^{88} +17.6573 q^{89} +7.26621 q^{90} -13.4324 q^{91} -2.19016 q^{92} +15.6614 q^{93} -7.13736 q^{94} +2.38940 q^{95} +2.82194 q^{96} +14.0099 q^{97} -2.18037 q^{98} -32.2957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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